Surprisingly, the relict cosmological constant has a crucial influence on properties of accretion discs orbiting black holes in quasars and active galactic nuclei. We show it by considering basic properties of both the geometrically thin and thick accretion discs in the Kerr - de Sitter black-hole (naked-singularity) spacetimes. Both thin and thick discs must have an outer edge allowing out ow of matter into the outer space, located nearby the so called static radius, where the gravitational attractionof a black hole is balanced by the cosmological repulsion. Jets produced by thick discs can be significantly collimated after crossing the static radius. Extension of discs in quasars is comparable with extension of the associated galaxies, indicating apossibility that the relict cosmological constant puts an upper limit on extension of galaxies.